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(2x+1)(x+3)=9
We move all terms to the left:
(2x+1)(x+3)-(9)=0
We multiply parentheses ..
(+2x^2+6x+x+3)-9=0
We get rid of parentheses
2x^2+6x+x+3-9=0
We add all the numbers together, and all the variables
2x^2+7x-6=0
a = 2; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·2·(-6)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{97}}{2*2}=\frac{-7-\sqrt{97}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*2}=\frac{-7+\sqrt{97}}{4} $
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